The inversion of the y-axis is irrelevant here.
The default tick generator is trying to give you a reasonable number of ticks while evenly spacing them out. It's actually trying to put a zero as the first tick, but since you set the minimum to one, the first tick isn't shown.
You can get around this by creating your own tick generator. Here's a sample tick generator based on the default one that will replace zero with one as the first tick.
http://jsfiddle.net/Lkkxgexj/